CamCASP/Notes/1

CamCASP => Notes => Rotating integrals

1. Rotating integrals

CamCASP allows the User fine control over integrals and the density-fitting. This can be used to save time (and also debug) during certain types of calculations. So, if you need to evaluate integrals like the density-overlap integral for many dimer configurations, here are two ways of doing it:

• Redoing the density-fitting for each dimer configuration

Set DF
  Redo-df-on-rotation
End

Begin DF-ints
  Int Type OVRL Desc XAXB Print
End
Begin E1exch
  NO-E1exch
  Overlap integrals without constraints
End

Edit CD
  Rotate by 90 degrees about 0.0 0.0 1.0
  Show geometry and MOs
  Update MOs & Geom
  Show geometry & MOs
End

Begin DF-ints
  Int Type OVRL Desc XAXB Print
End
Begin E1exch
  NO-E1exch
  Overlap integrals without constraints
End

This works as follows:

1. We first tell the code to repeat density-fitting even if all that has happened is that a molecule has been rotated.
2. Next you could perform the density-fitting for the two molecules, but it will be automatically done when the DF-INTS is called.
3. Use the DF-INTegral module to calculate the integral. Here is it the overlap integral needed to calculate the density-overlap. The density-overlap is a special kind of integral that is not calculated in this module.
4. Use the E1EXCH module to calculate the density-overlap integrals. The NO-E1exch command prevents the calculation of the first-order exchange energy which is calculated by default.
5. Now rotate one of the molecules (CD). The UPDATE MOs & GEOM command must be used to update the molecule geometry and the molecular orbitals.
6. You could re-do the density-fitting for the rotated molecule (CD), but it will be automatically done by DF-INTS...
7. Recalculate the overlap integrals, but this time include the ROTATE option that will rotate them so as to be consistent with the previously calculated density-fitting solution.
8. And repeat the calculation of the denisty-overlap integrals.

This is a wasteful procedure. A better way is as follows...

• Doing the density-fitting only once & rotating integrals

Set DF
  Redo-df-on-rotation  False
End

Begin DF-ints
  Int Type OVRL Desc XAXB Print
End
Begin E1exch
  NO-E1exch
  Overlap integrals without constraints
End

Edit CD
  Rotate by 90 degrees about 0.0 0.0 1.0
  Show geometry and MOs
  Update
  Show geometry & MOs
End

Begin DF-ints
  Int Type OVRL Desc XAXB Print Rotate
End
Begin E1exch
  NO-E1exch
  Overlap integrals without constraints
End

This works as follows:

1. We first stop the code from repeating density-fitting if all that has happened is that a molecule has been rotated.
2. Next you could perform the density-fitting for the two molecules, but it will be automatically done when the DF-INTS is called.
3. Use the DF-INTegral module to calculate the integral. Here is it the overlap integral needed to calculate the density-overlap. The density-overlap is a special kind of integral that is not calculated in this module.
4. Use the E1EXCH module to calculate the density-overlap integrals. The NO-E1exch command prevents the calculation of the first-order exchange energy which is calculated by default.
5. Now rotate one of the molecules (CD). The UPDATE command must be used to update the molecule geometry. But do not update the molecular orbitals (i.e., don't use UPDATE MOs).
6. Recalculate the overlap integrals, but this time include the ROTATE option that will rotate them so as to be consistent with the previously calculated density-fitting solution.
7. And repeat the calculation of the denisty-overlap integrals.

--alston 18:39, 17 October 2008 (BST)